Factorize:
$a^{2} x + a b x + a c + a b y + b^{2} y + b c$

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Solution

Using common factor method :
$= a^{2} x + a b x + a b y + b^{2} y + a c + b c$
$= a x (a + b) + b y (a + b) + c (a + b)$
$= (a + b) [a x + b y + c]$
Hence, the answer is $(a + b) [a x + b y + c] .$

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